Here, \(\mathcal {R}\)  is a regularizer which encodes prior information about the desired solution and \(\frac{1}{2} {\mathbf {K}x- y^\delta }^2\)  plays the role of a data-discrepancy measure. Classically, regularizers have been hand-crafted, including \(L^2\) -penalties, sparse regularization techniques or total variation [1]}, [2]}, [3]}. While such hand-crafted regularizers are often convex and hence global minima can be computed by classical convex optimization, hand-crafted priors typically lack adaptability to available data.
